In this study, design and thermal analysis of a medium-frequency transformer with ferrite N87 core have been carried out using finite-element analysis software. A thermal model of the medium-frequency transformer is generated and analyzed with different cooling methods. In addition, it is proposed to attach additional heat sinks at the top and bottom of the transformer core. Effects of these additional heat sinks on cooling performance and sizing of the transformer are investigated. Furthermore, the cooling capacity of the proposed material is investigated, depending on the air flow velocity for the forced-air cooling method. Thus, more realistic behavior of the ferrite N87 material is obtained for a medium-frequency transformer with 35 kVA rated power and 10 kHz operating frequency. Moreover, electromagnetic and thermal analyses are carried out through linked simulations. The heat distribution in the core including saturation effect is also investigated in detail.